The global positioning system rebecca smyth

1. The Global Positioning
System
Rebecca C. Smyth
April 17 - May 2, 2001

2. GPS-Global Positioning System
• Department of Defense navigation system
• Triangulation from a constellation of 24
satellites broadcasting pseudo-randomly
coded signals on radio waves (speed of light)
from known positions (given by orbital
ephemerides) at very precise time intervals.
• Satellites at altitude of 20,200 km;
distributed in 6 orbital planes with inclination
of 55 degrees to equator
• Four or more satellites visible at all times
anywhere in world.
• First satellite launched February 22, 1978

3. GPS-Global Positioning System
• Coordinates are determined using known
satellite positions and the measured
distances between those satellites and the
unknown position at a precise time.
• A GPS receiver determines its position in
three dimensions: x, y, and z. The height (z)
coordinate is different from the horizontal
coordinates (x and y) both in how it is defined
and how accurately it can be measured.

4. Orbit
Geocenter
Earth
Receiver
?
K
n
o
w
Satellite Positioning

5. GPS Data - Signal Types
• Single frequency C/A-code (Civilian Access;
Coarse Acquisition) - 1.023 MHz chipping rate
• Single frequency P code (Precise;
Protected, or Precision); becomes Y-code
when encrypted - 10.23 MHz chipping rate;
only 2 satellites have P-code, the rest have Y-
code.
• Dual frequency Carrier Phase (L1 and L2) -
L1 frequency = 1575.42 MHz (λ = 19 cm), L2
frequency = 1227.6 MHz (λ = 24.4 cm).
• L1 carries C/A code, P code, and
Navigation message
• L2 carries P code only

6. GPS Solutions
• Simple, Typical, or Pseudo-range -
accuracy of +/- 100m with SA turned on or +/-
20 to 25m with SA off (ex. uncorrected
solutions using GeoExplorer or Garman
receivers)
–SA (Selective Availability) - dithering or
introduction of a clock timing error and
introduction of an orbital error.
• Differential - correction uses a terrestrial
point with precisely known position between
the satellites and the unknown points to
reduce errors.

7. GPS Solutions
• Real-time differential - correction using a
virtual base station (ex. Omnistar satellite
system or coast guard system)
• Post processed differential - correction
using base station of known coordinates
using single frequency C/A-code or dual
frequency carrier phase (ex. corrected
GeoExplorer, Trimble 4000ssi or Ashtech Z-
12)

8. - Solve for position of field station
relative to reference station.
- Eliminate common errors including
Selective Availability
- Reference station computes
pseudorange corrections for field
stations
Differential GPS Positioning
1000
1000 ?
GPS reference station
- known position
GPS field station
- unknown position

9. GPS Solution Details
• Pseudo-range solution (single difference
solution)- difference between time of signal
transmission from satellite and time of arrival
at receiver times speed of light (c ~ 3 x 108
m/sec);
• Double-difference solutions - linear
combinations of difference solutions; further
reduces errors by canceling out differences
between receivers, satellites, and epochs.
• Widelaning of the dual frequency -
differencing between the phase observations
made on L1 and L2.

10. Pseudo-Range Measurements
1000
+1
-1
+1
-1
T
Code generated by Satellite
Code generated by Receiver
Pseudorange = C*T
9
6
3
12
9
6
3
12

11. +1 -1
Carrier Phase Measurements
Carrier signal generated by Receiver
Carrier signal generated by Satellite
9
6
3
12
9
6
3
12
1000



phase difference

12. 9
6
3
12
1000
9
6
3
12
Carrier signal generated by Satellite
Phase range = N
N = Phase Ambiguity
Carrier Phase Ambiguity




13. Ambiguity Resolution
Resolve N's if we
- observe a few satellites for a long time or
- observe many satellites for a short time.

14. Single Differencing
prange(1,A) = CT(1,A) + tropo + ion + SV1 clock + RcvrA clock
- prange(1,B) = CT(1,B) + tropo + ion + SV1 clock + RcvrB clock
prangeA-B
=
C

-
C
+
RcvrA clock
-
RcvrB clock
prange(2,A) = CT(2,A) + tropo + ion + SV2 clock + RcvrA clock
- prange(2,B) = CT(2,B) + tropo + ion + SV2 clock + RcvrB clock
prange2,A-B
=
C

-
C
+
RcvrA clock
-
RcvrA clock
1000 1000
SV1
Rcvr A Rcvr B
SV2

15. Double Differencing
prange2,A-B
=
C

-
C
+
RcvrA clock
-
RcvrA clock
prangeA-B
=
C

-
C
+
RcvrA clock
-
RcvrB clock
prange-2A-B


C

-
C

- C
+
C
1000 1000
SV1
Rcvr A Rcvr B
SV2
-

16. GPS Solution Errors
• Satellight clocks
• SA
• Ephemerides
(satellight orbits)
• Atmospheric delays
• Multipathing
• Receiver clocks
GPS Error Sources
Receiver Clock Error
1000
L1
L2
9
6
3
12
9
6
3
12
Satellite Clock Error including
Selective Availability
Ionospheric refraction
Multi-pathing
Tropospheric Delay
Satellite Orbit Error
?
? ?

17. Error Budget (m)
Standard GPS Differential GPS
Satellight clocks 1.5 0
Orbit errors 2.5 0
Ionosphere 5.0 0.4
Trophosphere 0.5 0.2
Receiver noise 0.3 0.3
Multipath 0.6 0.6
SA 30.0 0

18. Coordinate Systems
• Conventional Terrestrial Reference System (CTRS) aka
Geocentric XYZ aka Earth Centered Earth Fixed (ECEF) -
origin at mass center of earth; z-axis aligned with mean
spin axis of earth; x-axis points toward the Greenwich
Meridian; y-axis is at right angles to x in direction
determined by right-hand rule.
• Universal Transverse Mercator (UTM) - meters; 60 N-S
elongate zones each 6 degrees in longitude; zone 1 starts
at 180 degrees longitude and they proceed east; x is called
easting and y is called northing; the origin of x and y in
UTM is the intersection of the equator and central
meridian, where x=500,000m (numbers decrease to east
and increase to west) and y=10,000,000m (numbers
increase to north and decrease to south); easting normally
precedes northing.
• Geographic Coordinates (latitude and longitude) =
ellipsoidal coordinates

19. GPS-Vertical Measurements
• Ellipsoid - surface of an ellipsoid of
revolution
• Ellipsoidal Heights - Based on WGS-84
(World Geodetic System last updated in 1984)
• Orthometric Heights - height above the
geoid; equipotential surface that closely
approximates the idealized surface of the
oceans (aka) height above mean sea level
(AMSL)
• Geoidal Undulations - geoidal height which
is the geoid-ellipsoid separation. Geoid
models are based on satellight and terrestrial
gravity data.

20. Ellipsoid and Geoid Heights
h
H
N
Earth’s
surface
Geoid
Ellipsoid
h, measured by GPS
N, Geoid anomaly provided by GEOID99 model
H, orthometric height = h - N
GEOID99 converts GPS ellipsoidal heights to NAVD 88 orthometric heights

21. GPS-Vertical Datums
• GPS height - ellipsoid height given in CTRS
• WGS-84 (World Geodetic System last updated in
1984) - defines the reference ellipsoid and the CTS
used for GPS work.
• NGVD67 - (National Geodetic Vertical Datum)
attempted to combine geoid and AMSL corrections;
was an attempt to position the reference ellipsoid
so that it best approximated the geoid. This datum
is no longer used.
• NAVD88 - (North American Vertical Datum) an
orthometric height datum. Based on a reference
ellipsoid, the surface of which approximates the
geoid over the region covered by the datum.